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Figure 2. Distributions of
channel types. (A) Cumulative
histograms of single channel amplitudes observed in patches
from oocytes coinjected with WT
and mutant cRNAs at the various
ratios (W:M) indicated. Current
amplitudes, measured at −60
mV, were taken from fits of the
amplitude histograms as shown
in Fig. 1 C with a mixture of
Gaussian functions. Dotted lines
indicate the mean of each group,
whose value is given in the bottom panel. (B) Histograms showing the number of observed
channels belonging to each
group. The data were fitted to a
binomial distribution (solid lines)
and the probability ratio that
generated the maximum likelihood is given as Pm/Pw in each
panel.
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Figure 3. Two types of amplitude histograms from tail currents. (A) A representative current trace from the M4 channel.
The holding potential was −100
mV. The dashed line indicates
zero current level; data were filtered at 1 kHz. Two thresholds
(dotted lines) were used to detect
the times when current crossed
10 and 90% of the fully open current level during deactivation at
−100 mV. (B) Tail histogram,
made by accumulating all the
data points in the tail current
time course from 148 sweeps,
scaled to units of milliseconds
per picoampere. Superimposed
are Gaussian functions fitted to
each peak (dotted curves) and
their sum (solid curve). The peak
position of each Gaussian gives
an estimate of each current amplitude, and the area under each
Gaussian gives an estimate of the
mean dwell time of that state.
This histogram included sweeps
in which the channel failed to deactivate during the 200-ms recording period; thus, the sublevel components are artifactually reduced in area. (C)
Transition histogram, made by
accumulating those data points
that fell between the final crossing of the 90% threshold and the
subsequent crossing of the 10%
threshold. This histogram shows
more clearly the dwells in sublevels. (D) Simulated current steps
of unit amplitude after Gaussian
filtering (1 kHz, solid curve ; 5
kHz, dotted curve) show finite
dwell times in the transition
range. (E) Scaled amplitude histograms from the time courses in
D. Notice that the apparent dwell
times from a current step at 1
kHz are much shorter than those
obtained from the tail transitions
in C.
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Figure 4. Sublevels in each
channel type. (A) Representative single-channel deactivation
time courses at −100 mV. The repolarization to −100 mV preceded the beginning of each
trace, which shows only the vicinity of the recording where the deactivation transition occurred.
Dotted lines indicate baselines.
Data were filtered at 1 kHz except for W4, which was filtered at
5 kHz. Two sweeps from a M2W2L
channel and two sweeps from a
M2W2H channel are shown to
demonstrate two types of closing
transitions, one through sub2
and sub1, the other through
sub2′. Two W4 sweeps are also
presented (with expanded time
scale as shown). The left sweep
shows a transition with an obvious dwell in sub2, the right sweep
has no apparent dwells in sublevels. (B) Tail histograms at −100
mV, from 148 (M4), 223 (M3W),
298 (M2W2L), 165 (M2W2H), 40
(MW3), and 412 (W4) sweeps, respectively. (C) The corresponding transition histograms, obtained as in Fig. 3 C. Thresholds
defining the transitions were 10
and 90% except in the case of
W4, where the thresholds were
set at 15 and 85% of the fully
open current amplitude.
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Figure 5. Voltage dependence of the mean lifetimes in each current level. Mean dwell times of the open (A), sub2 (B), and sub1 (C)
states were estimated from Gaussian fits to transition histograms as in Fig. 4. Mean dwell times for the M4 channel were measured by threshold analysis (Zheng and Sigworth, 1997); the histogram analysis of M4 currents yielded similar results. The standard deviations are also
shown for each channel type at −100 mV. The numbers of channels measured for each channel type are: W4, n = 2; MW3, n = 5; M2W2L,
n = 4; M2W2H, n = 3; MW3, n = 2; W4, n = 2. The dotted curve in each panel represents the prediction from the kinetic scheme for the M4
channel given by Zheng and Sigworth (1997). The brief lifetimes of sublevels in MW3 and W4 channels precluded their measurement at
voltages below −120 and above −80 mV.
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Figure 6. Closing transitions at −100 mV are characterized by
the time the final transition spent between 90 and 10% of the current amplitude. Superimposed on the histograms are results of
maximum-likelihood fits to each measured value assuming that
the closures are either instantaneous transitions from fully open
current to zero current level (whose measured dwells are approximated by a Gaussian distribution, Eq. 5) or transitions through
one (for M2W2L, MW3, and W4) or two (for M4 and M3W) sublevels,
whose measured dwells are approximated by one or two exponential distributions convolved with a Gaussian probability density
function with the same variance (Eq. 6). The time constant of the
exponential functions and the fraction A0 of the instantaneous
component are: M4, τ1 = 12.1 ms, τ2 = 3.2 ms, 8%; M3W, τ1 = 6.9
ms, τ2 = 0.9 ms, 4%; M2W2L, τ = 3.6 ms, 17%; MW3, τ = 1.1 ms,
18%; W4, τ = 0.26 ms, 20%.
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Figure 7. Correlation of dwell times in sublevels. Activation transitions at −60 mV were filtered at 1 kHz and dwells in each sublevel were measured by a pair of thresholds that bracketed it. Only
those sweeps showing a unidirectional progression of conductance
levels were counted. Each plotted point represents the apparent
dwell times in sub1 and sub2, except in the right-hand M2W2L graph
where dwells in sub2′ are plotted against the total time spent in the
two larger sublevels. In each graph, the dotted curves represent
the locus of points obtained from simulations in which one or the
other sublevel is skipped during activation. In all channel types,
there were many transitions having nonzero dwells in both current
levels, except for the M2W2L channel, for which only 2 of 167 deactivations showed a long dwell in both the sub2–sub1 level and the
sub2′ level. The M2W2H channels behaved similarly to the M2W2L
channels (data not shown).
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Figure 8. Current amplitudes
with Rb+ ion as the charge carrier. (A) Representative tail currents of M2W2L (top) and W4 (bottom) channels recorded at −100
mV with 140 mM Rb+ ion in the
pipette solution. (B) Tail histograms of M2W2L and W4 channels. (C) Transition histograms
accumulated from the final closing transitions. The two peaks in
the M2W2L histogram have areas
of 5.0 and 3.1 ms, respectively.
The peak in the W4 histogram
has an area of 0.6 ms. (D) Ratio
of Rb+ to K+ current amplitudes
in the fully open level and in sublevels, measured at −100 mV.
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Scheme I.
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Scheme II.
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Scheme III.
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Figure 9. Mean lifetime of each current level depends on the
number of mutant subunits. The number of channels measured is
given in parentheses. Values from M2W2H channels are presented
as dotted symbols to distinguish them from those of M2W2L channels; for these two channel types, the sub2′ dwells are also plotted
(▵). Solid lines are fits to the lifetimes at −100 mV of an exponential function in which n is the number of mutant subunits as expected from Eq. 9. The k values are 0.90 (Open), 1.01 (Sub2), and
1.04 (Sub1). The dotted line represents the predicted lifetime of
the open state assuming that each subunit undergoes independent
transitions (Eq. 8). In this case, the transition rates (βm and βw) of
mutant and WT subunits were taken from the mean open time (t)
of the corresponding homomultimeric channels as βx = 1/(4tx).
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Figure 10. Hypothetical free energy profiles for M4 (solid curve)
and W4 channels (dotted curve), drawn with gating charge movement as the reaction coordinate. (A) Energy profile during channel activation at −60 mV. (B) Energy profile during deactivation at
−120 mV. The free energy change for each transition and the associated charge were calculated from the kinetic model of M4
channels (Zheng and Sigworth, 1997). The free energy differences
between M4 and W4 channels were calculated from the mean lifetimes of each state. The free energy at transition states was taken to
be the same between M4 and W4 for simplicity, and because the entry into conducting states (the first latency) is essentially unaffected by the mutation (Zheng and Sigworth, 1997).
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Figure 11. Two activation gating schemes. (A) The scheme of Zagotta et al. (1994b) is shown, in which a single subunit undergoes two
voltage-dependent conformational transitions (inset) to reach a permissive state (○ and •). Subunit transitions occur independently, with
the exception of a slowed transition from the open state 14 to state 13. The scheme has been modified to identify sublevels sub1 and sub2
with states in which two or three subunits are in the permissive state. (B) The scheme is modified to include a distinct transition (dotted line)
that follows activation of the subunits. This allosteric transition is assumed to switch between nonconducting states and open states having
different conductances. The equilibrium constants θs1, θs2, and θo are greatly increased by the T442S mutation. In both schemes, the conducting states are represented by • and ▴.
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